Study on Krasnoselskii's Fixed Point Theorem for Caputo-Fabrizio Fractional Differential Equations
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Date
2020
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Springer
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Abstract
This note is concerned with establishing existence theory of solutions to a class of implicit fractional differential equations (FODEs) involving nonsingular derivative. By using usual classical fixed point theorems of Banach and Krasnoselskii, we develop sufficient conditions for the existence of at least one solution and its uniqueness. Further, some results about Ulam-Hyers stability and its generalization are also discussed. Two suitable examples are given to demonstrate the results.
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Shah, Kamal/0000-0002-8851-4844
ORCID
Keywords
Krasnoselskii'S Fixed Point Theorem, Caputo-Fabrizio Fractional Differential Equations, Hyers-Ulam Stability, Artificial intelligence, Class (philosophy), Fractional Differential Equations, Generalization, Theory and Applications of Fractional Differential Equations, Invertible matrix, Mathematical analysis, Krasnoselskii’s fixed point theorem, Fixed Point Theorems in Metric Spaces, Differential equation, Banach fixed-point theorem, Machine learning, QA1-939, FOS: Mathematics, Fixed-point theorem, Stability (learning theory), Functional Differential Equations, Anomalous Diffusion Modeling and Analysis, Hyers–Ulam stability, Banach space, Fixed Point Theorems, Applied Mathematics, Fractional calculus, Pure mathematics, Caputo–Fabrizio fractional differential equations, Fixed point, Applied mathematics, Computer science, Picard–Lindelöf theorem, Modeling and Simulation, Physical Sciences, Geometry and Topology, Uniqueness, Mathematics, Ordinary differential equation, Fractional ordinary differential equations, Fractional derivatives and integrals, Hyers-Ulam stability, Applications of operator theory to differential and integral equations, Caputo-Fabrizio fractional differential equations, Krasnoselskii's fixed point theorem
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Fields of Science
02 engineering and technology, 01 natural sciences, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics
Citation
Eiman...at all (2020). "Study on Krasnoselskii's fixed point theorem for Caputo-Fabrizio fractional differential equations", Advances in Difference Equations, Vol. 2020, No. 1.
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Q1
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OpenCitations Citation Count
21
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Advances in Difference Equations
Volume
2020
Issue
1
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